\( sin \bigg (\frac{\pi}{3} - sin^{-1} (\frac{1}{2}) \bigg) \) is equal to \[ \begin{array} ((A) \: \frac{1}{2} \quad & (B)\: \frac{1}{3} \\ (C)\: \frac{1}{4} \quad & (D) \: 1 \end{array} \]

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